应用高斯分布来解决异常检测问题（二）

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在文章应用高斯分布来解决异常检测问题（一）中对如何使用高斯分布来解决异常检测问题进行了描述，本篇是使用R编程实现了第一篇中所描述的两个模型：多个一元高斯分布模型和一个多元高斯分布模型。

一、 多个一元高斯分布模型

 1 ## parameters:
 2 ##     x  -  a vector, which is the data of new samples.
 3 ##     X  -  a matrix, which stores samples‘ data.
 4 ##     parameterFile - path of paramter file,
 5 ##                     the paramter file stores the paramters of the MultiUnivariate Norm model.
 6 ##     isTraining - flag, TRUE will trigger the training,
 7 ##                        FALSE will skip the training.
 8 funMultiUnivariateNorm <- function(x, X = NULL, parameterFile = ".MultiUnivariateNorm", isTraining = FALSE)
 9 {
10     if (isTraining == TRUE) {
11         if (is.null(X) == TRUE) {
12             cat("X is NULL, MultiUnivariateNorm model Can‘t be trained\n")
13             return
14         }
15         numOfSamples <- dim(X)[1]
16         numOfFeatures  <- dim(X)[2]
17
18         vectrMean <- colMeans(X)
19         vectrSD <- numeric(0)
20         for (i in 1:numOfFeatures) {
21             vectrSD[i] <- sd(X[,i])
22         }
23
24         ## write the parameters to the file
25         ##   1st line is means divided by one blank
26         ##   2nd line is SDs divided by one blank
27         matrixMeanSD <- matrix(c(vectrMean, vectrSD), ncol=numOfFeatures, byrow=TRUE)
28         # checking of parameterFile leaves to write.table
29         write.table(x=matrixMeanSD, file=parameterFile, row.names=FALSE, col.names=FALSE, sep=" ")
30     } else {
31         matrixMeanSD <- read.table(file=parameterFile)
32         matrixMeanSD <- as.matrix(matrixMeanSD)
33         vectrMean <- matrixMeanSD[1,]
34         vectrSD <- matrixMeanSD[2,]
35     }
36
37     vectrProbabilityNewSample <- dnorm(x, mean = vectrMean, sd = vectrSD, log = FALSE)
38     prod(vectrProbabilityNewSample)  # probability of the new sample
39 }

二、 一个多元高斯分布模型

 1 ## Before using this function the package mvtnorm need to be installed.
 2 ## To install package mvtnorm, issuing command install.packages("mvtnorm")
 3 ## and using command library(mvtnorm) to load the package to R workspace.
 4 ##
 5 ## parameters:
 6 ##     x  -  a vector, the data of one samples that need to be calculate the output by the MultiUnivariate Norm model.
 7 ##           a matrix, each line is one sample that need to be calculate the output by the MultiUnivariate Norm model.
 8 ##     X  -  a matrix, which stores samples‘ data.
 9 ##     parameterFile - path of paramter file,
10 ##                     the paramter file stores the paramters of the MultiUnivariate Norm model.
11 ##     isTraining - flag, TRUE will trigger the training,
12 ##                        FALSE will skip the training.
13 funMultivariateNorm <- function(x, X = NULL, parameterFile = ".MultivariateNorm", isTraining = FALSE)
14 {
15     if (isTraining == TRUE) {
16         if (is.null(X) == TRUE) {
17             cat("X is NULL, MultivariateNorm model Can‘t be trained\n")
18             return
19         }
20
21         vectrMean <- colMeans(X)
22         matrixSigma <- cov(X)
23         ## write the parameters to the file
24         ##   1st line is means divided by one blank
25         ##   from the 2nd line to the last line are variances divided by one blank
26         matrixMeanCov <- rbind(vectrMean, matrixSigma)
27         # checking of parameterFile leaves to write.table
28         write.table(x=matrixMeanCov, file=parameterFile, row.names=FALSE, col.names=FALSE, sep=" ")
29     } else {
30         matrixMeanCov <- read.table(file=parameterFile)
31         matrixMeanCov <- as.matrix(matrixMeanCov)
32         vectrMean <- matrixMeanCov[1,]
33         matrixSigma <- matrixMeanCov[c(2:dim(matrixMeanCov)[1]),]
34     }
35
36     dmvnorm(x, mean = vectrMean, sigma = matrixSigma, log = FALSE) # probability of the new samples37 }